Source code for ht.conv_packed_bed

'''Chemical Engineering Design Library (ChEDL). Utilities for process modeling.
Copyright (C) 2016, Caleb Bell <Caleb.Andrew.Bell@gmail.com>

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__all__ = ['Nu_packed_bed_Gnielinski', 'Nu_Wakao_Kagei', 'Nu_Achenbach',
           'Nu_KTA']

[docs]def Nu_packed_bed_Gnielinski(dp, voidage, vs, rho, mu, Pr, fa=None): r'''Calculates Nusselt number of a fluid passing over a bed of particles using a correlation shown in [3]_ and cited as from [1]_ and [2]_. Likely the best available model as the author of [1]_ is the same as [2]_ and [3]_. .. math:: Nu = f_a Nu_{sphere} .. math:: Nu_{sphere} = 2 + \sqrt{Nu_{m,lam}^2 + Nu_{m,turb}^2} .. math:: Nu_{m,lam} = 0.664Re^{0.5} Pr^{1/3} .. math:: Nu_{m,turb} = \frac{0.037Re^{0.8} Pr}{1 + 2.443Re^{-0.1}(Pr^{2/3} -1)} .. math:: Re = \frac{\rho v_s d_p}{\mu \epsilon} Parameters ---------- dp : float Equivalent spherical particle diameter of packing [m] voidage : float Void fraction of bed packing [-] vs : float Superficial velocity of the fluid [m/s] rho : float Density of the fluid [kg/m^3] mu : float Viscosity of the fluid, [Pa*s] Pr : float Prandtl number of the fluid [] fa : float, optional Fator increasing heat transfer [] Returns ------- Nu : float Nusselt number for heat transfer to the packed bed [-] Notes ----- `fa` is a factor relating how much more heat transfer happens than would normally, around one sphere. For spheres of the same size, :math:`f_a = 1 + 1.5(1-\epsilon)`. For cylinders with l/d ratio of 0.24 < l/d < 1.2 use fa = 1.6. For cubes, use fa = 1.6 For Raschig rings, use `fa` = 2.1 For Berl saddles, use `fa` = 2.3. fa is calculated with the relationship for spheres if not provided. Confirmed with experimental data for a range of :math:`1E-1 < Re <1,000` and :math:`0.4 < Pr < 1000` for spheres. Limits are smaller for other shapes. Examples -------- >>> Nu_packed_bed_Gnielinski(dp=8E-4, voidage=0.4, vs=1, rho=1E3, mu=1E-3, Pr=0.7) 61.37823202546954 References ---------- .. [1] Gnielinski, V. (1981) "Equations for the calculation of heat and mass transfer during flow through stationary spherical packings at moderate and high Peclet numbers". International Chemical Engineering 21 (3): 378-383 .. [2] Gnielinski, V. (1982) "Berechnung des Warmeund Stoffaustauschs in durchstomten ruhenden Schuttungen". Verfahrenstechnik 16(1): 36-39 .. [3] Gnielinski, V. in G esellschaft, V. D. I., ed. VDI Heat Atlas. 2nd ed. 2010 edition. Berlin; New York: Springer, 2010. ''' Re = rho*vs*dp/mu/voidage Nu_lam = 0.664*Re**0.5*Pr**(1/3.) Nu_turb = 0.037*Re**0.8*Pr/(1 + 2.443*Re**-0.1*(Pr**(2/3.)-1)) Nu_sphere = 2 + (Nu_lam**2 + Nu_turb**2)**0.5 if fa is None: fa = 1.0 + 1.5*(1.0 - voidage) return fa*Nu_sphere
[docs]def Nu_Wakao_Kagei(Re, Pr): r'''Calculates Nusselt number of a fluid passing over a bed of particles using a correlation shown in [1]_ and also cited in the review of [2]_. Relatively rough, as it has no dependence on voidage. .. math:: Nu = 2 + 1.1Pr^{1/3}Re^{0.6} Parameters ---------- Re : float Reynolds number with pebble diameter as characteristic dimension, [-] Pr : float Prandtl number of the fluid [] Returns ------- Nu : float Nusselt number for heat transfer to the packed bed [-] Notes ----- Fit for Re from 3 to 3000; claimed reasonableness of fit to to 1E6. Examples -------- >>> Nu_Wakao_Kagei(2000, 0.7) 95.40641328041248 References ---------- .. [1] Wakao, Noriaki, and Seiichirō Kagei. Heat and Mass Transfer in Packed Beds. Taylor & Francis, 1982. .. [2] Abdulmohsin, Rahman S., and Muthanna H. Al-Dahhan. "Characteristics of Convective Heat Transport in a Packed Pebble-Bed Reactor." Nuclear Engineering and Design 284 (April 1, 2015): 143-52. doi:10.1016/j.nucengdes.2014.11.041. ''' return 2 + 1.1*Pr**(1/3.)*Re**0.6
[docs]def Nu_Achenbach(Re, Pr, voidage): r'''Calculates Nusselt number of a fluid passing over a bed of particles using a correlation shown in [1]_ and also cited in the review of [2]_. .. math:: Nu = [(1.18Re^{0.58})^4 + (0.23\left(\frac{Re}{1-\epsilon} \right)^{0.75})^4]^{0.25} Parameters ---------- Re : float Reynolds number with pebble diameter as characteristic dimension, [-] Pr : float Prandtl number of the fluid [] voidage : float Void fraction of bed packing [-] Returns ------- Nu : float Nusselt number for heat transfer to the packed bed [-] Notes ----- Claimed value for Re/ε < 7.7E5 Developed with tests performed in a wind tunnel at conditions up to 30 bar. Examples -------- >>> Nu_Achenbach(2000, 0.7, 0.4) 117.70343608599121 References ---------- .. [1] Achenbach, E. "Heat and Flow Characteristics of Packed Beds." Experimental Thermal and Fluid Science 10, no. 1 (January 1, 1995): 17-27. doi:10.1016/0894-1777(94)00077-L. .. [2] Abdulmohsin, Rahman S., and Muthanna H. Al-Dahhan. "Characteristics of Convective Heat Transport in a Packed Pebble-Bed Reactor." Nuclear Engineering and Design 284 (April 1, 2015): 143-52. doi:10.1016/j.nucengdes.2014.11.041. ''' return ((1.18*Re**0.58)**4 + (0.23*(Re/(1-voidage))**0.75)**4)**0.25
[docs]def Nu_KTA(Re, Pr, voidage): r'''Calculates Nusselt number of a fluid passing over a bed of particles using a correlation shown in [1]_ and also cited in the review of [2]_. .. math:: Nu = 1.27\frac{Pr^{1/3}}{\epsilon^{1.18}}Re^{0.36} + 0.033\frac{Pr^{0.5}}{\epsilon^{1.07}}Re^{0.86} Parameters ---------- Re : float Reynolds number with pebble diameter as characteristic dimension, [-] Pr : float Prandtl number of the fluid [-] voidage : float Void fraction of bed packing [-] Returns ------- Nu : float Nusselt number for heat transfer to the packed bed [-] Notes ----- 100 < Re < 1E5; 0.36 < ε < 0.42; D/d > 20 with D as bed diameter, d as particle diameter; H > 4d with H as bed height. Examples -------- >>> Nu_KTA(2000, 0.7, 0.4) 102.08516480718129 References ---------- .. [1] Reactor Core Design of High-Temperature Gas-Cooled Reactors Part 2: Heat Transfer in Spherical Fuel Elements (June 1983). http://www.kta-gs.de/e/standards/3100/3102_2_engl_1983_06.pdf .. [2] Abdulmohsin, Rahman S., and Muthanna H. Al-Dahhan. "Characteristics of Convective Heat Transport in a Packed Pebble-Bed Reactor." Nuclear Engineering and Design 284 (April 1, 2015): 143-52. doi:10.1016/j.nucengdes.2014.11.041. ''' return (1.27*Pr**(1/3.)*Re**0.36/voidage**1.18 + 0.033*Pr**0.5/voidage**1.07*Re**0.86)